Marshall was born in Chesterfield on 22 April 1929. His family moved to Blackpool, and Marshall joined Arnold School on a county scholarship. He turned down a place at Balliol College, Oxford, on the grounds that the facilities' heating was not good enough. Instead, in 1947 he joined Manchester University, reading Politics and Economics, and graduated in 1950. He attended lectures by Harold Laski and was asked to prepare them for publication, which he did under the title Reflections on the Constitution.
His first book, Parliamentary Sovereignty and the Commonwealth, was published in 1957. He described "sovereignty" as "an institutional arrangement resting upon an idea, and the idea is one which has philosophical (and even theological) implications". In 1959, his second book, co-authored by Graeme Moodie, was entitled Some Problems of the Constitution and dealt with ministerial responsibility. He examined the controls on government and the means of redress of the citizen against the state. He was elected a fellow and tutor in Politics at Queens's College, Oxford, in 1957, where he stayed until his retirement in 1999.
- Dennis Kavanagh (30 June 2003). "Obituary: Geoffrey Marshall". The Guardian. Retrieved 12 October 2011.
- "Obituaries: Geoffrey Marshall". The Daily Telegraph. 10 July 2003. Retrieved 12 October 2011.
- Vernon Bogdanor (1 July 2003). "Obituaries: Geoffrey Marshall". The Independent. Retrieved 12 October 2011.